%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV688-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:08:57 AM UTC 2026
% Result : Unsatisfiable 29.91s 4.36s
% Output : CNFRefutation 29.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 18 unt; 0 def)
% Number of atoms : 26 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-5 aty)
% Number of variables : 70 ( 27 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(c_229,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring]) ).
fof(cls_inverse__inverse__eq_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(c_HOL_Oinverse__class_Oinverse(VAR_0),hAPP(c_HOL_Oinverse__class_Oinverse(VAR_0),VAR_1)) = VAR_1
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Odivision__ring(VAR_0) ),
file('theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(c_239,plain,
( hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Odivision__ring(A) ),
inference(clausify,[status(thm)],[cls_inverse__inverse__eq_0]) ).
fof(cls_COMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_COMBS__def_0) ).
cnf(c_344,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
fof(cls_COMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_4),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_345,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_346,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_Suc__n__not__n_0,axiom,
! [VAR_0] : hAPP(c_Suc,VAR_0) != VAR_0,
file('theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(c_906,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(c_1324,plain,
( hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_239,c_229]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(c_1488,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero]) ).
cnf(c_1791,plain,
hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A,
inference(resolve,[status(thm)],[c_1488,c_1324]) ).
cnf(c_1838,plain,
hAPP(c_COMBS(c_COMBC(A,B,C,D),E,F,V6,V7),V8) = hAPP(hAPP(A,hAPP(E,V8)),V8),
inference(paramod,[status(thm)],[c_345,c_344]) ).
cnf(c_2093,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_346,c_906]) ).
cnf(c_3028,plain,
hAPP(c_COMBS(c_COMBC(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A,B,C),c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),D,E,F),V6) = hAPP(V6,V6),
inference(paramod,[status(thm)],[c_1791,c_1838]) ).
cnf(c_3030,plain,
hAPP(A,E) != hAPP(c_COMBB(c_Suc,A,B,C,D),E),
inference(copy,[status(thm)],[c_2093]) ).
cnf(c_3029,plain,
$false,
inference(resolve,[status(thm)],[c_3028,c_3030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV688-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 14:44:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3979156 was started by sandbox on n007,
% 0.19/0.45 % Sat Sep 26 14:44:39 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/0.56
% 0.23/0.56 % From the command line: assign(max_seconds, 300).
% 29.91/4.36
% 29.91/4.36 % given #500 (I,wt=35): 960 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),A),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # tptp_name(cls_differentiable__sum_0) # clausal_fof(1). [assumption].
% 29.91/4.36
% 29.91/4.36 % given #1000 (I,wt=31): 1607 hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(217,a,224,a)].
% 29.91/4.36
% 29.91/4.36 % SZS status Unsatisfiable for theBenchmark
% 29.91/4.36
% 29.91/4.36 % Proof 1 at 3.48 (+ 0.29) seconds.
% 29.91/4.36 % Length of proof is 13.
% 29.91/4.36 % Level of proof is 4.
% 29.91/4.36 % Maximum clause weight is 28.000.
% 29.91/4.36 % Given clauses 1257.
% 29.91/4.36
% 29.91/4.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------